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A358977
Numbers that are coprime to the sum of their primorial base digits (A276150).
7
1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 53, 54, 55, 57, 58, 59, 61, 62, 63, 67, 69, 71, 73, 74, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98, 101, 102, 103, 106, 107, 109, 110
OFFSET
1,2
COMMENTS
Numbers k such that gcd(k, A276150(k)) = 1.
The primorial numbers (A002110) are terms. These are also the only primorial base Niven numbers (A333426) in this sequence.
Includes all the prime numbers.
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 7, 59, 603, 6047, 60861, 608163, 6079048, 60789541, 607847981, 6080015681... . Conjecture: The asymptotic density of this sequence exists and equals 6/Pi^2 = 0.607927... (A059956), the same as the density of A094387.
LINKS
EXAMPLE
3 is a term since A276150(3) = 2, and gcd(3, 2) = 1.
MATHEMATICA
With[{max = 4}, bases = Prime@Range[max, 1, -1]; nmax = Times @@ bases - 1; sumdig[n_] := Plus @@ IntegerDigits[n, MixedRadix[bases]]; Select[Range[nmax], CoprimeQ[#, sumdig[#]] &]]
PROG
(PARI) is(n) = {my(p=2, s=0, m=n, r); while(m>0, r = m%p; s+=r; m\=p; p = nextprime(p+1)); gcd(n, s)==1; }
CROSSREFS
Subsequences: A000040, A002110.
Similar sequences: A094387, A339076, A358975, A358976, A358978.
Sequence in context: A076786 A298540 A326535 * A284892 A319315 A325467
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 07 2022
STATUS
approved